Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 4, 970 - 981, 06.08.2021
https://doi.org/10.15672/hujms.750167

Öz

Kaynakça

  • [1] K. Burde, Das Problem der Abzählreime und Zahlentwicklungen mit gebrochenen Basen, J. Number Theory 26 (2), 192–209, 1987.
  • [2] L. Halbeisen and N. Hungerbühler, The Josephus Problem, Journal de Thèorie des Nombres de Bordeaux, 9, 303–318, 1997.
  • [3] F. Jakóbczyk, On the Generalized Josephus Problem, Glasg. Math. J. 14, 168–173, 1973.
  • [4] T. F. Josephus, The Jewish War (translated by William Whiston).
  • [5] A.M. Odlyzko and H.S. Wilf, Functional iteration and the Josephus problem, Glasg. Math. J. 33 (2), 235–240, 1991.
  • [6] J.W. Park and R. Teixeira, Serial Execution Josephus Problem, Korean J. Math. 26 (1), 1–7, 2018.
  • [7] W.J. Robinson, The Josephus Problem, Math. Gaz. 44 (347), 47–52, 1960.
  • [8] F. Ruskey and A. Williams, The Feline Josephus Problem, Theory Comput. Syst. 50 (1), 20–34, 2012.
  • [9] A. Shams-Baragh, Formulation of the Extended Josephus Problem, in: National Computer Conference, December 2002.
  • [10] S. Sharma, R. Tripathi, S. Bagai, R. Saini and N. Sharma, Extension of the Josephus Problem with Varying Elimination Steps, DU Journal of Undergraduate Research and Innovation 1 (3), 211–218, 2015.
  • [11] R. Teixeira and J.W. Park, Mathematical Explanation and Generalization of Penn and Teller’s Love Ritual Magic Trick, Journal of Magic Research 8, 21–32, 2017.
  • [12] N. Thèrialut, Generalizations of the Josephus Problem, Util. Math. 58, 161–173, 2000.
  • [13] D. Woodhouse, The Extended Josephus Problem, Rev. Mat. Hisp.-Amer. 33 (4), 207– 218, 1973.

Block Josephus Problem: When the reality is more cruel than the old story

Yıl 2021, Cilt: 50 Sayı: 4, 970 - 981, 06.08.2021
https://doi.org/10.15672/hujms.750167

Öz

In the Josephus Problem, there are $n$ people numbered from $0$ to $n-1$ around a circle and proceeding around the circle every second person is executed until no one survives. Determining where to stand on the circle to be the last survivor is called the Josephus Problem. In this paper, we present a generalized version of the Josephus Problem and study cases where multiple executions occur at each iteration. Especially, we focus on the Block Josephus problem where the number of skips and the number of executions are the same. In particular, we present nonrecursive formulas for the initial positions of survivors in the Block Josephus Problem.

Kaynakça

  • [1] K. Burde, Das Problem der Abzählreime und Zahlentwicklungen mit gebrochenen Basen, J. Number Theory 26 (2), 192–209, 1987.
  • [2] L. Halbeisen and N. Hungerbühler, The Josephus Problem, Journal de Thèorie des Nombres de Bordeaux, 9, 303–318, 1997.
  • [3] F. Jakóbczyk, On the Generalized Josephus Problem, Glasg. Math. J. 14, 168–173, 1973.
  • [4] T. F. Josephus, The Jewish War (translated by William Whiston).
  • [5] A.M. Odlyzko and H.S. Wilf, Functional iteration and the Josephus problem, Glasg. Math. J. 33 (2), 235–240, 1991.
  • [6] J.W. Park and R. Teixeira, Serial Execution Josephus Problem, Korean J. Math. 26 (1), 1–7, 2018.
  • [7] W.J. Robinson, The Josephus Problem, Math. Gaz. 44 (347), 47–52, 1960.
  • [8] F. Ruskey and A. Williams, The Feline Josephus Problem, Theory Comput. Syst. 50 (1), 20–34, 2012.
  • [9] A. Shams-Baragh, Formulation of the Extended Josephus Problem, in: National Computer Conference, December 2002.
  • [10] S. Sharma, R. Tripathi, S. Bagai, R. Saini and N. Sharma, Extension of the Josephus Problem with Varying Elimination Steps, DU Journal of Undergraduate Research and Innovation 1 (3), 211–218, 2015.
  • [11] R. Teixeira and J.W. Park, Mathematical Explanation and Generalization of Penn and Teller’s Love Ritual Magic Trick, Journal of Magic Research 8, 21–32, 2017.
  • [12] N. Thèrialut, Generalizations of the Josephus Problem, Util. Math. 58, 161–173, 2000.
  • [13] D. Woodhouse, The Extended Josephus Problem, Rev. Mat. Hisp.-Amer. 33 (4), 207– 218, 1973.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Jang-woo Park 0000-0002-2855-2902

Ali Dogan 0000-0001-8650-9358

Ricardo Teıxeıra 0000-0002-3412-1965

Yayımlanma Tarihi 6 Ağustos 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 4

Kaynak Göster

APA Park, J.-w., Dogan, A., & Teıxeıra, R. (2021). Block Josephus Problem: When the reality is more cruel than the old story. Hacettepe Journal of Mathematics and Statistics, 50(4), 970-981. https://doi.org/10.15672/hujms.750167
AMA Park Jw, Dogan A, Teıxeıra R. Block Josephus Problem: When the reality is more cruel than the old story. Hacettepe Journal of Mathematics and Statistics. Ağustos 2021;50(4):970-981. doi:10.15672/hujms.750167
Chicago Park, Jang-woo, Ali Dogan, ve Ricardo Teıxeıra. “Block Josephus Problem: When the Reality Is More Cruel Than the Old Story”. Hacettepe Journal of Mathematics and Statistics 50, sy. 4 (Ağustos 2021): 970-81. https://doi.org/10.15672/hujms.750167.
EndNote Park J-w, Dogan A, Teıxeıra R (01 Ağustos 2021) Block Josephus Problem: When the reality is more cruel than the old story. Hacettepe Journal of Mathematics and Statistics 50 4 970–981.
IEEE J.-w. Park, A. Dogan, ve R. Teıxeıra, “Block Josephus Problem: When the reality is more cruel than the old story”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 4, ss. 970–981, 2021, doi: 10.15672/hujms.750167.
ISNAD Park, Jang-woo vd. “Block Josephus Problem: When the Reality Is More Cruel Than the Old Story”. Hacettepe Journal of Mathematics and Statistics 50/4 (Ağustos 2021), 970-981. https://doi.org/10.15672/hujms.750167.
JAMA Park J-w, Dogan A, Teıxeıra R. Block Josephus Problem: When the reality is more cruel than the old story. Hacettepe Journal of Mathematics and Statistics. 2021;50:970–981.
MLA Park, Jang-woo vd. “Block Josephus Problem: When the Reality Is More Cruel Than the Old Story”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 4, 2021, ss. 970-81, doi:10.15672/hujms.750167.
Vancouver Park J-w, Dogan A, Teıxeıra R. Block Josephus Problem: When the reality is more cruel than the old story. Hacettepe Journal of Mathematics and Statistics. 2021;50(4):970-81.